2011•Logical Methods in Computer ScienceOpen access

Semantics of Typed Lambda-Calculus with Constructors

Barbara Petit

Abstract

We present a Curry-style second-order type system with union and intersection types for the lambda-calculus with constructors of Arbiser, Miquel and Rios, an extension of lambda-calculus with a pattern matching mechanism for variadic constructors. We then prove the strong normalisation and the absence of match failure for a restriction of this system, by adapting the standard reducibility method.

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Key concepts: System F, Typed lambda calculus, Simply typed lambda calculus, Lambda calculus, Church encoding, Intersection (aeronautics), Dependent type, Extension (predicate logic)